Aircraft: B737
Phase of flight: Initial Approach
Anomaly: Aircraft Equipment Problem Less Severe

While being vectored for Visual Approach to Runway XX at ZZZ; the First Officer called for Flaps 5. I set the Flap Handle to 5 and about the same time ATC called our base turn. It was shortly afterward that I realized the flaps had barely moved; even though the handle was in the 5 detent. The indicators were split; 1 at 0; and the other at about 1/2 degree (I don't recall L/R). I pointed this out to the First Officer and we agreed to abandon the approach and work the problem through the QRH. While being vectored by ATC; we referenced the Trailing Edge Flap Asymmetry Checklist. This checklist directed us to bring the flap handle back to the Up position; which in turn led us to the Trailing Edge Flaps Up Landing Checklist. At that point I made sure the First Officer had the flight controls and ATC; and I contacted Dispatch/Maintenance through ZZZ OPS frequency. I informed them of our condition and told them we would probably need to divert to ZZZ1 in order to have a longer runway. We began to run weight and balance numbers and brake cooling data for Runway XY at ZZZ1. Dispatch was doing the same; but also ran numbers for Runway XX at ZZZ. They informed us that we would have a stopping margin of about 1;500 ft. with Autobrake Max. We went ahead and confirmed this by running the numbers ourselves; but neither one of us was comfortable landing on the shorter runway because we also had the Number 2 thrust reverser inoperative. This was something that was already on an MEL. Another big concern was brake cooling and potential for blowing tire fuse plugs.We both felt like the safest and most conservative choice was the longer runway at ZZZ1. I was fully aware that it would be inconvenient for everyone involved but had to remind myself of our operational priorities and their order. Dispatch; ATC; Flight Attendants; and Passengers were all fully informed of our situation. We [requested priority handling] with ATC and requested vectors for a 25 mile final to give us time to finish the QRH procedures which required us to deploy the leading edge flaps via the alternate method. I assumed control of the aircraft about 35 miles from the airport. We finished the QRH and made the high speed approach and landing on Runway XY without incident. CFR (Crash Fire Rescue) was waiting and we had them inspect the tires and brakes. They noted nothing of concern and based on my brake application at about 130 kts.; we were able to proceed to a gate that had been coordinated for us. On shutdown we noted low B-system quantity of 74 and an RF displayed. Defects were entered in the logbook and per coordination from the Operations Center; the passengers and crew eventually deplaned; cleared Immigration and Customs; and boarded ground transportation for ZZZ.This was just an unfortunate flap malfunction. I don't think it was preventable. While on downwind; descending through 3;500 ft. to 2;000 ft. for Visual Approach to Runway XX into ZZZ; we attempted to configured to flaps 5. One flap did not move and the other flap extended to about a half of a degree. We coordinated with ATC to level off at 3;000 ft. and got vectors while we worked the problem. We started with the Trailing Edge Flap Asymmetry Checklist. This checklist drove us to move the flap handle back to 'Up'. The flaps remained in an asymmetric condition so; per the QRH; we transitioned to the Trailing Edge Flaps Up Landing Checklist. At that point; the Captain began coordinating with Dispatch; while the First Officer continued to fly. After looking at the performance and brake cooling data at both ZZZ and ZZZ1; we decided to divert to ZZZ1 in order to land on a longer runway. Although we had the performance data to land at ZZZ; given the combination of the no flap landing and #2 thrust reverser MEL (inherited from a previous flight) doing so would have required a max braking effort; longer brake cooling period (over one hour) and ultimately a smaller margin of safety. We coordinated with ATC to fly a 25 mile visual straight in to Runway XY at ZZZ1. Additionally; we [requested priority handling with ATC]; coordinated with Dispatch; and informed the passengers and flight attendants of the situation. We finished the Trailing Edge Flaps Up Landing Checklist; deploying the leading edge devices through the alternate flaps extension procedure; and the Captain landed on Runway XY; applying brakes at about 130 kts. We taxied off the runway; had the emergency vehicles check the brake temperatures (which they assessed as normal); and uneventfully taxied to the gate. At the gate; we noticed that the number 2 hydraulic quantity was low (the quantity indicated about 75 with an 'RF' annotated). Neither this condition nor any other hydraulic abnormality alerted throughout the flight. After coordinating for Customs and offline support; we ended the flight without further incident. B737 flight crew reported a flap extension failure that resulted in a diversion.